#non linear axiomatic systems

[caustic-splines]

I can be soft and vulnerable, I am willing to let you hurt me because I love you and trust you. I know you are passionate I rediscovered part of the reason why I love you so much. Your love is discrete, inverse pun intended but both homonyms applicable in this analogy. It is private, our unique form of expression

But it is also literally discrete, like recent quantum gravity field theories I may or may not have a hand in. My mind craves clarity, more so, it craves discrete caustic lines an planes. I would like to be like that every day. I want my heart to be in the inner of a particle accelerator bit-west two colliding high energy beams. All the crazy spins and flavor's of normal, charming, and even exotic sub atomic particles smashing apart, smashing together, twirling off in random spirals based on EM fields. That is who I am, not a particle reactor,

but every emergent self and extended phenotype aspect of my projects, world views, emotions, experiences, thoughts and behaviors.

Do you really want to see what I have seen when I was manic, I will make a brief outline, which barely does it justice, nor was the experience worth it in my mind

I saw reality

Across all multi scale layers of objective, subjective, abstract existance. Both perceived and externally existing.

Across all of these non-linear and semi-non empirical scales

Ontology categories of conscious awareness -5 Planc Quantized Wireframe -4 Subatomic Interactions -3 Electron Orbitals -2 Biochemical Interactions -1 Neurological Activity 0 Perception Input and basic awareness/dispersibility [(x n-1…n5) State of dissociation of whatever perceptual order or unconsciousness/dreaming] 1 Awareness of perception and SV 2 Awareness of perception in context or awareness of awareness -Xa Intrapersonal models 3 Awareness of self, regarding one's cognitive topography -Xb Allocentric models 4 Aware of a disruptive axiomatic shift recursively impacting various areas and fidelity of one's consciousness -Xc Global and Orbital Cyberphysical Memetogeographic Space -Xd Cosmology 5 Aware of a fundamental change in perception or PMC affecting POV. Shift in paradigm -Xe Uber Universes/5D+ EGC splines (ego/exo/allo) centric/ totality of EISOA over CT0-9

In the context of modular frames, of which I have objectively real working minimal level of knowledge in all of these domains, some reaching PhD levels of mastery

1 Technology

1 Applied Science/Applied Uses of TSECpm Phenomenon 2 ~Sustainable, Agricultural, Ecological and Environmental 3 Fabrication, Trade/Craft, and Intra/Inter Human Skill/Functionality 4 Military/Security/OMA7 5 Educational, Knowledge, Cognitive, Cybernetics, and Information, DT/PT 6 Electronics, Computers, Software, Spectrum, AI 7 Industries, Material Collection, Cyclical/NA: Supply Chains, Accounting 8 Skills, Fabrication, Synthesis, and Patents, Logistics 9 Civil, Nationality, Era, Civilian, State, and Structural 0 Future Technology/Other

2 Philosophy

1 Logic 2 Epistemology 3 Aesthetics 4 Politics 5 Dialectics, Critical Thinking, and Rhetoric 6 Ethics and Morality 7 Metaphysics and Ontology 8 Meta Linguistics 9 Applied Philosophy 0 Analytic Philosophy/Other

3 Engineering

1 Nuclear Engineering 2 Chemical Engineering 3 Biological Engineering/Medical Engineering 4 Environmental Engineering 5 Systems Engineering  and Cybernetics 6 Electrical Engineering 7 Mechanical Engineering 8 Industrial Engineering  9 Civil Engineering    0 Personal Engineering/Cognitive Engineering/Experience Engineering, ME0002/0013/0034/0049, Other

4 General-Cultural

1 Interactive Mediums/4, 3//Middle World IO MR Interaction/Hobbies/EISOA interactions 2 Geography, Culture, [[SMPH/ME 1/Experiment 0032 TSeCIVii|Experiment 0032 TSeCIVii]] 3 Occult/Niche Allusion/Metaphor 4 Physical, Mental, and Cognitive Skills 5 Day to Day Functionality, House Keeping, BH, and Normative and Exotic Behavior (Anomolies vs Normative Phenomena, timescale/PoF independent) 6 Law, Rules, Conduct, Ethology 7 Finance and Business/Institutions/VSM/States/Governing Bodies 8 Dynamic PPF+/-PoV, People of Interest, UJSF 9 Politics and Society – Collective Conscious Gestalt 0 UM, Pop culture/other, (**(almost) ALL EISOA can be contained in USF(EISOA Correlate))

5 Frameworks

1 Gestalt, Non Gestalt (AS/S)_, Spatial and/or Temporal Patterns, and Non-Modular and Modular Ontology, Shapes, Objects, Sounds,  Qualia Framed Experiences which can be Axiomatized (basically an intersystem link to 1, 1 to enable dual +y/1, 1 functionality) 2 PT/MR Mathematical and Mapping/Fields Competition and Game Theory, NWF (applying [[Experiment 0024 LoUtrix]] to 1, 1) 3 UJSF/Society and Culture/Cyberphysical Environments (EISOA cybersocial considertations) 4 TSECpm, +y/PT, Exocognition/LLM integration 5 Mindmap/MEs, and Modelling, Psychology/EISOA, Thought Traces/2, 5/AE/DABPAx (self imposed 3, 4 for the meta task of utilizing +y effectively) 6 Experiential and PMC/5, x /1, 1/3, 1/2, x/PE (1, 1-2-5-6/2, x subjective experience. MM08, x 7 IESOA, CABS, Frames, (OMA7), Fuzzy Logic, 3, 4/VSMs/SMPH Optimal Scheduling and [[Unsignificant Sentience/Mental Experiments/Experiment 0005 Chewing Gum Loading Dock|Experiment 0005 Chewing Gum Loading Dock]] [[SMPH/ME 1/Experiment 0058 Just in Time 1, 31, 5AE+Y|Experiment 0058 Just in Time 1, 31, 5AE+Y]] HMI workflow (EIOA on IS) 8 Language and Linguistics, Metaphor/SWHs, [[SMPH/ME 1/Experiment 0012 Fractal Cosmic Regression|Experiment 0012 Fractal Cosmic Regression]] 9 Cognition, Learning, and Experience/ 09, x 0 Axiomatic Systems, Perspective Theory/other, PoFs

6 Science

1 Physics 2 Astrophysics and Cosmology 3 Chemistry 4 Biology 5 Interdisciplinary/System Science 6 Health Sciences 7 Earth Sciences 8 Formal Science 9 Social Sciences 0 Other

7 Abstract Constructs, Functions, and Relationships

1 Set Theory 2 Ontology 3 Epistemology 4 Metaphysics 5 Digital/Cognitive Twins 6 Abstract Object Mapping 7 Abstract Object Manipulating 8 Elucidating Abstract Space into IS space and vice versa 9 Metaphysical Abstract Space Workshop, CA 0 Communicable and interactive Abstract Entities/Engineering of the Abstract

At the same time, world building a sci fi universe and multiple systems of systems that would be abstracted and logically patterned into some of the most influential books in human history.

The fourth book? You are a main character you wrote your own part you played. It is probably the first case of hypersituatal fictional historic non fiction that guided the development of humanity culturally and scientifically. I became a living fictive, I had all of my human rights removed, but not my natural rights.

When you see everything, you can change everything

I had reality fuck it's way into my brain and leave gaping wounds that have never healed. I can handle some rough love dear

Maybe one day I will be able to share the light show

[darkmaga-returns]

Something that increasingly occupies my thoughts is the degree to which a progressive or linear view of history maps onto reality as it is, without historical biases and ideological framing. On its face, it seems like a non-starter of an issue; after all, I’m typing this piece on an electronic device connected to a ‘‘World Wide Web’��� that would have astonished and bamboozled people just a few decades ago. Regarding technology, the linear view of history reigns supreme; we have traveled the long and winding path of development and incremental improvements and advanced to the digital age and the pocket-sized supercomputer. There is no ‘‘un-inventing’’ technology, it is argued; thus, the cyclical view of history, if it were ever true, has been broken.

My view on such pride in technological wonders is that the higher we ascend via these increasingly complex mechanisms, the more painful the landing will be when the complexity becomes too great. The opposite view is that in Artificial Intelligence, which is to say another complex system, we shall be able to maintain the structures for the rest of time and that an escape velocity will be reached, no turning back, or hard landings need ever occur.

Scant regard is ever given to the human clay within the machine. It is taken as axiomatic that we, along with digital networks and supply chains, will adapt and become more "modern" alongside our devices. This world picture assumes that because TikTok and Uber Eats exist, archaic religious impulses and mad conceptions of millenarian prophesies and destinies will fade into the past.

It must be so because the divine spark of progress guides us all to the horizon of infinite improvement and human potential.

[art-of-mathematics]

is mathematics dealing with absolute truth?

That question is really thrilling to answer, to be honest.

We have to define 'absolute truth' first.

If we consider this "absolute truth" as logical consistency, then I'd like to introduce Gödel's Incompleteness Theorems:

Gödel's Incompleteness Theorems, for instance, state that mathematics will never be complete, because it will always have parts that cannot be proven. Either it is incomplete, but consistent, or complete but inconsistent (in form of being self-referent).

Mathematics cannot prove itself by its own rules, WITHIN its own system.

As for another track of thoughts/perspctive: (Now it becomes an utter mess... And I am sorry for leaping between multiple different conceptions rn. My thinking process IS like what I describe here - a sort of "extraction process" of "truth", or correct and exact thoughts. )

The only "absolute truth" there is, is actually that there is none - as a kind of "structure" at least, as in a "static", non-chaotic linear axiomatic system (Classical logic). When it comes to non-linear axiomatic systems [networks] (inserting chaos theory in meta-math - neat feedback-loop INSIDE mathematics as recursive system itself btw) I would rather refer to such "truth" as a process of oscillating around the most exact reality description - the symmetry axis is hence the equilibrium state and the actual structure of absolute truth. But- this is exceeding the margin now - The absolute state is an information singularity I call "invertium". Reaching that equilibrium causes an 'inversion', a process of inner polarity. That recursive inner polarity IS that absolute truth.

Furtherly, I somehow sense a strange logical twisted mindfuck fusing Gödel's Incompleteness with my concepts on non-linear axiomatic [networks] (Quantum logic, in a sense). (Transcendence of a paradox, huh???)

Also, in regards of these trains of thought, "absolute truth" is what I would call a "superposed entangled state of all truths and lies" - like an information singularity. A state in which an Invertium happens - the indistinguishabilty of two extreme states - 100% dense information can't be distinguished from a 0% one. A singularity is hence, in a sense, an isolated [conservative] system itself, from a rough viewpoint.

What happens in this state? I suppose a desintegration of said information as "self/own complex", and integration of its information parts into its super-ordinate medium. (That is how I interpret entanglement) (The information strangely "dissolves"/integrates.)

Absolute truth bears every partial truth - and all partial truths, well, I would refer here to Feynman's Path integrals, virtual pairs in Feynman-diagrams and statistical mechanics.

And I am sorry for the confusion. Maybe one day I will be able to turn these highly compressed thoughts into fathomable chunks.

(In my upcoming book a lot of the concepts stated above will be some of the primary issues.)

[art-of-mathematics]

The interesting plot twist: These complex underlying structures consist of simple patterns of the "processes" they emerge from. It's like the perfect embodyment of math being a fractal construct itself, a complex of self-similarity, with patterns in processes that always replicate or/and interfere themselves.

The entire fundament of math for example, formal logic, especially non-linear axiomatic systems, is ruled by the results of the application of itself: for non-linear logic: results like chaos theory as example. It is like a somewhat literal feedback-loop between recursive (in a way 'nested') mathematical principles itself.

Mathematics, on itself is somewhat recursively self-referring and self-similar.

This makes me think about the connection between Gödel's incompleteness and certain similarities to conceptions about fractals. What is self-similarity, for instance? What is it in concrete? What is a fractal pattern in regards of information, in regards of an axiomatic approach? As an information transform process (which, in a way, is a non-linear axiomatic approach), a fractal pattern consists of primarily four aspects: self-reference, self-replication, self-interference, self-organizsation/self-simplification. If you add conceptions of 'levels' this leads back to certain interpretations regarding Gödel's incompleteness theorems about recursion, self-reference and a 'metascape' - yet, I don't really know at the moment how the parts I try to connect here will fit together with more details and more rigor. But my intuition senses a clear connection to be honest. And indulging in further elaboration seems more fruitful the deeper I dig.

Also: non-linear axiomatic systems have the interesting side-effect of their propositions not being binary, as the literal feedback loops result in probabilistic behavior of these axiomatic systems. Axiomatic networks are far more interesting than overly simplified linear axiomatic systems with binary nature.

It sounds heretic to make formal logic uncertain. But just as the interior angle of triangles is only equal to 180 in euclidean space, in a non-distorted space, non-linear logic is metaphorically like non-euclidean space here: the main frame of a version of 'cause-and-effect' of axiomatic systems is still there, but this chain reaction is extended to a 'network reaction'. Feedback loops fuck up the binary aspects.

To end this thought, a silly phrase fits:

Let's get into the metascape!

[compounds-of-my-wavefunction]

I am starting to digitally archive the art I have created throughout my life, and these were from 2013 [I was 15 back then.] , shortly after I found my way into my special interests of math and physics. I came from a merely "pseudo-/non-scientific interest section" back then - merely the philosophy branch and intersection of astronomy and astrology: duration of the orbit of planets around the sun/ repeating and changing of (interaction) patterns were my core interests in that particular interest/hyperfixation, which helped me build the bigger whole of what sums up my overall summarized "special interest cluster":

Interaction patterns and emergence in dynamical systems,

Axiomatization of dynamical systems,

Axiomatization of language, and language processing algorithms [computational linguistics and theoretical/cognitive neuroscience]

Axiomatic systems as information weaving system - fuzzy logic, and (non-linear, dynamical and emergent) quantum logic [new interpretation of axiomatic systems as dynamical and emergent information pattern]

Definition of special interest cluster: A collection of special interests that can be combined, are "interwoven" with each other and fit together like multiple puzzle pieces.

[scepticaladventure]

25  Gravity, Time and Light  6Sep18

Introduction In essence, Special Relativity is a systematic attempt to describe the physics of things that move fast, based up on postulates about light, and General Relativity is an attempt to include gravity. Hence a good question at the core of it all is “How does gravity affect the speed of light?” You might think this is a simple question but have a look at the Internet. Confusion reigns!

Sources of Confusion I think a lot of the confusion comes from lack of precision in the question. If Relativity has taught us anything it has taught us to be wary about simple questions about time, distance and speed. We have learnt we must first specify “Who is the observer and what is their situation?” We have learnt that the answers to simple questions about lengths, durations and speeds depend on how they are measured and in what circumstances are they measured - everything is relative.

Hence the speed of light in a strong gravitational field as measured by a local observer who is also embedded in that field might be different from a result obtained by a distant observer well away from the massive object creating the field.

It turns out that the speed of light is affected by a gravitational field, but so to (in fact hence) is local time keeping and so the local speed of light as measured by that local observer is the same as usual. The slowdown is undetectable. But from a more distant perspective the slowdown in the speed of light does become detectable.

Another source of confusion comes from the interrelated complexity between time, distance and speed. In a world where time can run fast or slow, distances can contract and Euclidean geometry may not hold true, the meaning of measurements and hence the quantification of physical properties becomes treacherous.

A third source of confusion comes from confused people teaching confused or confusing messages to innocent student, often with absolute conviction e.g. that the speed of light is a universal invariant that its always and everywhere the same.

What is Time? I was watching a science program the other day and the reporter asked a group of astrophysicists attending a theoretical physics conference in Ontario – what is time? Well they um’d and ah’d and said it was a difficult question and so on. They could not give a ready answer in plain English.

So let me have a go. Firstly the word itself covers two sorts of concepts – a way of tagging a river of events which may or may not be linked causally, and durations between events. Or to take a simple example – If you ask a time keeper at a sports event “What is the time?” she may reply “Do you mean the time of day, or the result of some competitor’s performance in an event?”

The underlying concept is causality. If an event A causes an event B then we say that A occurs before or simultaneously with Event B. No-one has ever witnessed causality running backwards, so we assume that it is a strictly one way affair.

When we come across physical phenomena with a repetitive regularity about them, such as the vibrations of a quartz crystal, we can use it to create a useful clock and hence create a measure of local time durations.

If we standardize such clocks to each other we can start to talk about the time more generally, and we can give an elementary answer to the question “what is the agreed exact time of day?”. But this is a man made convention. We have to be careful not to assume that our concepts can be applied well beyond the scope in which they were created. For example, we cannot assume that the whole Universe is embedded in some sort of all embracing river of time with a Universal standard clock somewhere.

Once we start to consider events on a cosmological scale, or in fast moving situations, we have come to understand that our normal day-to-day concepts of time do not suffice. Different observers can measure different time durations for the interval between the same two events. Time can be observed to run slow, not because clocks are distorted but because the finite speed of light means that the very concept of ‘what happens when’ needs to be reconsidered. Over and above that it turns out that time also runs slow in a gravitational field.

So time is nothing more than mankind’s attempt to quantify intervals between events. It is a manmade construct overlaid on reality, nothing more. It has no independent reality. In fact it can be considered to be a widely shared illusion. And a treacherous one at that.

Definitions and Standards of Measurement Let’s look at the simple equation c = D/T where c is the speed of light, D is a measure of distance travelled and T is a measure of time duration. For this to have any meaning we need an agreed way of measuring D and T and we need agreed units of measurement for both D and T. But where to start?

In the modern world our standards of measurement start with time.

Since the 1970’s there has been an international agreement that a standard second is defined by a set number of oscillations in the electromagnetic radiation (i.e. light) emitted by hyperfine transitions within Caesium 133 atoms held in certain conditions. A standard meter is then defined as being the distance travelled by this light in 1/299,792,458 standard seconds.

It then follows axiomatically that the standard speed of light is 299,792,458 meters per second. If nothing else this helps to pin down some terminology. But it does not mean that the actual speed of light will always be the same as the standard speed of light. A trivial example is if the light is travelling through glass. It’s slower. A more complicated example is if the light is travelling across a spiral galaxy.

Note that this whole approach to the definition of standards could have started in a different way. For example, a standard meter could have been defined as the distance between two scratches on a bar of metal held at a precise temperature in a specified location (e.g. Paris), and a standard second could then have been defined by the time taken for light to travel a set number of meters. Or a standard second could have been defined using an atomic clock and the speed of light could have been left out of it altogether, which is what used to happen before the current system was adopted.

There are three spatial dimensions and only one time dimension, so a democratic approach suggests we should start with defining distance and then move on to define time. Seriously though, length is a lot more observable and tangible than time. We can see and touch and run a ruler over the length of a thing. Time is invisible and intangible.

Timekeeping is always (as far as I can tell) based on motion of some sort, whether this be vibrations in a quartz crystal, the swing of a pendulum or the rotation of a planet. And since motion involves both distance and time, defining time durations based on the motions of things seems a little bit tricky. If time did not exist, how would we know anything was moving? The answer is that we could see things happening – things doing things to other things. Causality at work. But this would offer no guarantees about the nature of time. For example, if everything in the Universe speeded up by 10%, how could we tell?  

Furthermore, we know from experiments that time is affected by motion (Lorentzian time dilation) and by gravity (gravitational time dilation). So time is a rubbery phenomenon and in some situations it is a deceptive illusion.

Length is also affected by motion (Lorentzian contraction). This is a small effect in extreme circumstances, but it is nevertheless quite real. It was realized from experiments on the speed of light and came to become a key feature of the Theory of Special Relativity. But nobody, as far as I know, has been able to demonstrate length contraction in a simple experiment or demonstration. And I have never seen a photo-montage showing a Lorentz contracted object.

It is very difficult to hold up ruler against a physical object travelling at relativistic speeds in a straight line and be  able to record both ends at exactly the same time. The closest experiments I know of come from studies of high speed collisions between atomic nuclei at the Brookhaven Relativistic Heavy Ion Collider. The heavy nuclei have a non-zero radius and the dynamics of the collisions give the results expected if the nuclei are Lorentz contracted into disks. However, the Brookhaven accelerator is not a linear accelerator and this brings into play the theoretical complications of rotating and accelerated systems (see for example the Ehrenfest rotating disc paradox). Determining the effective radii of the ions is also problematical.

The three spatial dimensions of an object in spacetime are tangible. You can see and touch and measure lengths, widths and heights. You can put a ruler next to them. Time durations on the other hand are anything but simple, especially if the object is moving. You need to specify the situation of the observer very carefully. You need to carry the same clock from one event to the other or else to use a carefully synchronised set of clocks.

Time is a consequential parameter. It is the consequence of causality. At heart maybe the only thing you can be sure of is that Event A causes Event B, then Event A occurs before Event B. This also creates the Arrow of Time. In other words time is a one way phenomenon. You can never re-measure the exact same time interval, nor can you ever measure a time duration in back to front order.

The usual way to bridge from the world of tangible spatial dimensions to a world that involves time, motion, momentum and energy is to involve the speed of light.

What is an Inertial Reference Frame? After studying the results of experiments by Bradley, Eotvos, Roemer and Fizeau (and presumably Michelson and Morley, which he failed to acknowledge) Einstein simply postulated that that the speed of light in vacuum in an inertial reference frame is always the same (299,792.458 km/sec).

By inertial reference frame he meant one which is not accelerating, rotating or in a gravitational field. A frame in which test particles weigh nothing and stay still or travel in straight lines unless compelled by a force to do otherwise.

I think that an inertial reference frame is a an idealized concepts which is impossible to find in practice. Everything in the Universe is either spinning, accelerating or affected by gravity.  It was and still is common to say that an inertial reference frame is aligned to the “fixed stars”. However, no-one ever clarifies whether such stars are in our galaxy or beyond it, and what such stars can possible have to do with local physics anyway.

I all my reading I cannot find clarity about whether a satellite in orbit constitutes an inertial reference frame or not. The satellite is undoubtedly within a gravitational field or else it could not be orbiting. But the apparent effects of gravity are undone by the fact that the satellite is in free fall. Or you could consider the force of gravity to have been annulled by the effects of centrifugal acceleration. Either way you look at it test particles inside the satellite will be weightless. So are atomic clocks in this situation subject to gravitational time dilation or not?

I think this is a good question. If the answer is that the gravitational potential at which the satellite orbits does slow down the onboard observers’ clocks then they can determine whether they are free falling in gravity field by measuring the frequency of signals received from deep space, a pulsar say, on their local clock. If the signals are coming in too quickly then their clock is running slow. So they can tell that they are in fact free falling in a gravity field. This violates the Einstein Equivalence Principle, even though some authors will try to wriggle out of it by saying that the experiment is not a local one.

If the answer is no then it suggests that gravitational time dilation only occurs when matter has weight. It also suggests that a centrifugal acceleration can undo gravitational time dilation. Both aspects would be worth deep consideration. There would be interesting implications for the Clock Postulate (see an earlier essay).

As far as I can tell the answer is yes, clocks aboard an orbiting satellite are still subject to a degree of gravitational time dilation, quite apart from Special Relativity effects.

Apart from that an orbiting space station is still a potential candidate to be a localized inertial reference frame. But we have to worry about possible rotational effects.

Sagnac interferometers could be used to detect any spinning of the satellite. If the satellite is managed so that there is no spinning detected in any direction then I guess that the satellite is pretty close to being an inertial reference frame. Now let us look out of the windows of the satellite. It is generally accepted that if telescopes were positioned so that they point at very distant galaxies then those telescopes would remain pointed at those distant galaxies.

But then observers on board the satellite would perceive the Earth going round and round the satellite every orbit. And the Sun and nearly stars would all be going around and around too. So is the satellite spinning or not?

You can see that inertial reference frames are not easy to define in practice!

Einstein and the Speed of Light Between 1905 and 1911 Einstein concentrated on generalizing his description of physics and developed an approach/model that has become known as the Theory of General Relativity. By 1911 he had concluded that in the presence of gravity the speed of light is not a fixed invariant. His model of Special Relativity had to be qualified and elaborated upon. The measured speed of light in a gravitational field becomes a variable depending upon the reference frame of the observer.

His logic is contained in his paper On the Influence of Gravitation on the Propagation of Light', Annalen der Physik, 35, 1911. This predates the full description of his General Theory of Relativity by four years. The result he came up with was expressed mathematically as c’ = (1 + Φ/c2).c   where Φ is the gravitational potential relative to the point where the speed of light is measured.

In other words, light appears to travel slower in stronger gravitational fields. There is a more complete description in Section 3 of ‘The Meaning of Relativity', A. Einstein, Princeton University Press (1955).

In 1915 Einstein revised this calculation to be c’ = (1 + 2Φ/c2).c  In other words he decided the effect was twice a great as he first thought.

Unlike in the inertial reference frames of Special Relativity, the measured speed of light in gravitational fields depends upon the reference frame of the observer. What one observer sees as true, another observer sees as not true, or at least slightly different.

If you wanted to be mischievous you could say that Einstein’s Theory of Special Relativity is based upon his proposition that the speed of light is invariant, and his Theory of General Relativity is based upon his proposition that the speed of light is not invariant.

Time in a Gravity Well We know from the impressive achievements made in recent decades in developing GPS systems that atomic clocks at rest on the surface of the Earth run slower than identical clocks on orbiting satellites.

For GPS to work, atomic clocks on Earth have to be very well synchronised with identical clocks aboard specially designed satellites. There are a variety of relativistic effects in play but the main one is due to the fact that the earthbound clocks are in stronger gravity than the orbiting satellites. The effect of gravitation is slightly reduced by centrifugal accelerations caused by the spin of the Earth. The overall gravitational effect is about 45 microseconds per day.

The gravitational time dilation effect is then adjusted for smaller relativistic effects, the main one being a Special Relativistic time dilation because the satellites are moving fast relative to the earthbound clocks. This offsets the gravitational effect by about 7 microseconds per day, giving a net relative adjustment of 38 microseconds per day.

When the satellites were first deployed the scientists in charge were not totally confident how much fine tuning would be required to get perfect synchronisation, so they allowed for a large degree of post launch adjustment. Now they make most of the adjustments before launch.

Of course gravity can have a direct physical effect on clocks. For example, a pendulum clock could not work without it. But that it not what we are talking about here. We are talking about an impact on time itself.

The way I prefer to think about all this is to start with the experimental fact that gravity has an effect on the speed of light. Then I remind myself that the measure of time can be thought of as physical lengths divided by the speed of light. Hence time durations are affected by gravity. And then every physical quantity involving time, notably every form of energy, is also affected.

Shapiro Time Delay The Shapiro time delay effect, or gravitational time delay effect, is now regarded as one of the classic tests of General Relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return than they would if the mass of the object were not present. The time delay is caused by the slowing passage of light as it moves over a finite distance through a change in gravitational potential.

In “Fourth Test of General Relativity”, Physics Review Letters, 20 1265-1269, 1968, Irwin Shapiro wrote, “Because, according to the general theory, the speed of a light wave depends on the strength of the gravitational potential along its path, these time delays should thereby be increased by almost 2x10−4 sec when the radar pulses pass near the Sun. Such a change, equivalent to 60 km in distance, could now be measured over the required path length to within about 5 to 10% with presently obtainable equipment.”

This test was first confirmed by experiments that ‘bounced’ radar signals off the planet Venus when it was just visible on the far side of the Sun as seen from Earth. It has since been measured using Mercury as well, and also using satellites such as the Cassini probe.

Note that seen from afar the path taken by the photons is a curve in both directions. You might think that this is what makes them take longer, but that is not the best way to think of it. The photons are taking the quickest route possible, but they are still delayed by the presence of the gravity field of the Sun. They do actually slow down in the stronger gravity closer to the Sun.

Light in a Gravity Well If we throw a ball upwards in a gravity field the ball decelerates, comes to a temporary stop at the top of its trajectory, and falls again. If we throw it faster than the Earth’s escape velocity the ball can overcome the overall gravitational attraction of the Earth and fly off into space with a certain amount of residual velocity.

What happens to a photon ejected from the surface of the Sun? Several essays ago we discussed and decided that the photon arrives at its destination detector in a weakened state. By comparison to other photons we can deduce that it has less energy and momentum than when it started and the frequency of its effects upon being absorbed are slower. In other words it reveals that it has become red shifted.

Does this mean that photons must travel slower as they climb higher – just like the ball? No – not at all! In fact the opposite is true (to a tiny extent). In the above section we discussed that the speed of light is faster in a weak field than it is in a strong field, and this is an experimental fact. Therefore the speed of photons (as measured by a distant observer) actually increases as the photons move into a weaker and weaker gravitational field.

This seems paradoxical. The arriving photon is travelling faster when its arrives than when it started, as measured from afar, but it arrives with less energy than when it started.

To understand this I think it is useful to note that the speed of a photon (as observed from afar) has no bearing on its energy level. See my earlier essay about energy remaining the same when photons travel in media with different refractive indices. I think the energy of a photon is embodied in the packet of physical properties it takes with it rather than in the speed of that packet as deduced by an external observer.

So how then does the photon become weaker? And where did the energy that is no longer contained in the photon end up? In the example of the thrown ball, what is going on is that as the ball gains in potential energy it loses kinetic energy until eventually it stops moving for a moment and then starts to fall again. There is a tradeoff between potential energy and kinetic energy. The potential energy can be thought of a being stored in the gravitational interaction between the Earth and the ball.

Much the same thing seems to happen to a photon. As it gains potential energy it loses electro-magnetic energy so that when it arrives it is weaker (i.e. redshifted).

I think this is a partially adequate description of what happens. However, if you want to adopt the Einstein Equivalence Principle as literally true and in some ways a better description of reality, and if you want to replace the greatest force in the Universe with the mathematical trickery of curved spacetime, then you can also explain the result using the language of Doppler shifts related to accelerations in curved spacetime. It also gives the right answer, so it becomes a matter of choice which point of view you want to adopt.

If you do use Einstein’s General Relativity model then note that it is only the perturbation of the time term that is needed in order to come up with the observed results for gravitational redshifts. The full field equations are not needed and there is no need to call upon any warping in the spatial aspects of the spacetime geometry.

Textbook Conventions Textbook explanations of Special Relativity invariably adopt Einstein’s postulate that the speed of light is an invariant constant. Many go further and tidy up all their equations by putting c = 1 and measuring all distances in light-seconds. They then drop c out of all the equations. They also carry over this convention into General Relativity.

However, most of the interesting predictions and effects of General Relativity depend upon the speed of light not being an invariant constant. So (in my opinion) writing c=1 and then omitting it from the equations obscures and confuses the physics of interest. Likewise, defining the speed of light to be exactly 299,792,458 meters per second is confusing unless we call this the standard speed of notional light and allow for the fact that the actual speed of light is slightly different from this in nearly all situations of interest and experience.

Conclusions Light slows down in the presence of gravity and so it is not invariant. But what you measure as its speed depends on how you measure it. A local measurement will not detect any difference. The speed of light is fundamental to the concept, meaning and measurement of time. So unless you can get this sorted out in your own mind, your physics is destined to end up in a muddle. And you would not be alone!

[deomnibuscontradictionibus]

Circuitries, by Nick Land

LAND, Nick. Fanged Noumena: Collected writings 1987-2007. Edited by R. Mackay & R. Brassier. 3 ed. Urbanomic, 2014, pp. 289-318.

“Our human cam­ouflage is coming away, skin ripping oJff easily, revealing the glistening electronics.” (p.292)

“Since central nervous-systern functions -especially those of the cerebral cortex -are amongst the last to be technically supplanted, it has remained superficially plausible to represent technics as the region of anthropoid knowing corresponding to the technical manipulation of nature, subsumed under the total system of natural science, which is in turn subsumed under the universal doctrines of epistemology, metaphy:sics, and ontology. Two linear series are plotted; one tra.cking the progress of technique in historical time, and the other tracking the passage f rom abstract idea to concrete realization. These two series chart the historical and transcendental dominion of man. 

Traditional schemas which oppose technics to nature, to literate culture, or to social relations, are all domi­nated by a phobie resistance to the sidelining of human intelligence by the coming techno sapiens. Thus one sees the decaying Hegelian socialist heritage clinging with increasing desperation to the theological sentimentalities of praxis, reification, alienation, ethics, autonomy, and other such mythemes of human creative sovereignty. A Cartesian howl is raised: people are be.ing treated as things! Rather than as ... soul, spirit, the subject of history, Dasein? For how long will this infantillism be protracted?” (pp. 293-294)

“There is no real option between a cybernetics of theory or a theory of cybernetics, because cybernetics is neither a theory nor its object:, but an operation within anobjective partial circuits that r1eiterates 'itself' in the real and machines theory through the unknown. 'Production as a process overflows all ideal categories and f orms a cycle that relates itself to desire as an immanent principle.' (G. Deleuze and F. Guattari, Anti-Oedipus: Capitalism and Schkophrenia, Minnesota: University of Minnesota Press, 1983, p. 5.)  Cybernetics develops functionally, and not representa­tionally: a 'desiring machine, a partial object, does not represent anything' (Ibid., 47). (Its semi-closed assemblages are not descriptions but programs, 'auto'-replicated by way of an operation passing across irreducible exteriority. This is why cybernetics is inextricable from exploration, having no integrity transcending that of an uncomprehended circuit within which it is embedded, an outside in which it must swim. Reflection is always very late, derivative, and even then really something else.” (p. 296)

“Reality is immanent to the machinic unconscious: it is impossible to avoid cybernetics. 1We are already doing it, regardless of what we think. Cybernetics is the aggrava­tion of itself happening, and wha1tever we do will be what made us have to do it: we are doing things before they make sense.” (p. 297)

[superação do design e de toda teopolítica]

“Long-range positive feedback is neither homeostatic, nor amplificatory, but escalative. Where modernist cyber­netic models of negative and positive feedback are inte­grated, escalation is integrating or cyber-emergent. I t is the machinic convergence of uncoordinated elements, a phase-change from linear to non-linear dynamics. Design no longer leads back towards a divine origin, because once shifted into cybernetics it ceases to commensurate with the theopolitical ideal of the plan. Planning is the creationist symptom of underde:signed software circuits, associated with domination, tradition, and inhibition; with everything that shackles the future to the past. All planning is theopolitics, and theopolitics is cybernetics in a swamp.” (pp. 298-299)

“A machinic assemblage is cybernetic to the extent that its inputs program its outputs and its outputs program its inputs, with incomplete closure., and without reci­procity. This necessitates that cybernetic systems emerge upon a fusional plane that reconnects their outputs with their inputs in an 'auto-production of the unconscious' (Ibid, p. 26) [...] It is thus that machin:ic processes are not merely functions, but also sufficient conditions for the replenishing of functioning; immanent reprogrammings of the real, 'not merely functioning, but formation and autoproduction' (Ibid)” 

[para além da moral]

“Wiener, of course, was still a moralist: 

Those of us who have contributed to the new sci­ ence of cybernetics stand in a moral position which is, to say the least, not very çomfortable. We have contributed to the initiation of a new science which, as I have said, embraces technical developments with great possibilities for good or evil. (N. Wiener, Cybernetics or Control and Communication in the Animal and the Machine. NY: MIT Press, 1965, p. 28.)

Whilst scientists agonize, cybernauts drift. We no longer judge such technical developments from without, we no longer judge at all, we function: machined/machining in eccentric orbits about the technocosno. Humanity recedes like a loathsome dream.“ (pp. 209-300)

[superação do transcendental e do juízo; dominação X controle]

“Transcendental philosophy is the consummation of philosophy construed as the doctrine of judgment, a mode of thinking that finds its zenith in Kant and its senile dementia in Hegel. Its architecture is determined by two fundamental principles: the linear application of judgment to its object, form to intuition, genus to species, and the non-directional reciprocity of relations, or logical symmetry. Judgment is the great fiction of transcendental philosophy, but cybernetics is the reality of critique. 

Where judgment is linear and non-directional, cyber­netics is non-linear and directional. It replaces linear appli­cation with the non-linear circuit, and non-directional logical relations with directional rnaterial flows. The cybernetic dissolution of judgment i:s an integrated shift from transcendence to immanence, from domination to control, and from meaning to function. Cybernetic innovation replaces transcendental constitution, design loops replace faculties. This is why the cybernetic sense of control is irreducible to the traditional political conception of power based on a dyadic master/slave relation, i.e. a transcendent, oppo­sitional, and signifying figure of domination. Domination is merely the phenomenological portrait of circuit inef­ficiency, control malfunction, or stupidity. The masters do not need intelligence, Nietzsche argues, therefore they do not have it. It is only the confused humanist orientation of modernist cybernetics which lines up control with domination. Emergent control is not the execution of a plan or policy, but the unmanageable exploration that escapes all authority and obsoles:ces law. According to its futural definition control is guidance into the unknown, exit from the box.” (pp. 300-301)

[beyond psychoanalysis; beyond Oedipus]

“In its early stages psychoanalysis discovers that the unconscious is an impersonal machinism and that desire is positive non-representational flow, yet it 'remains in the precritical age' , (Deleuze and Guattari, Anti-Oedipus, p. 339) and stumbles before the task of an immanent critique of desire, or decathexis of society. Instead it moves in exactly the opposite direction: back nto fantasy, representation, and the pathos of inevitable frustration. Instead of rebuilding reality on the basis of the productive forces of the unconscious, psychoanalysis ties up the unconscious ever more tightly in conformity with the social model of reality. Embracing renunciation with a bourgeois earnestness, the psychoanalysts begin their robotized chant: 'of course vve have to be repressed, we want to fuck our mothers and kill our fathers' They settle clown to the grave business of interpretation, and all the stories lead back to Oedipus: 'so you want to fuck your mother and kill your father:' (Ibid.)” (pp. 302-303)

“The word 'schizophrenia' has both a neurotic and a schizophrenic usage. On the one hand condemnation, on the other propagation.“ (p. 305)

“Since the neuroticization of schizophrenia is the molecular reproduction of capital1, by means of a re­axiomatization ( reterritorialization) of decoding as accu­mulation, the historical sense of psychoanalytic practice is evident. Schizophrenia is the pattern to Freud's repres­sions, it is that which does not qualify to pass the screen of Oedipal censorship.” (p. 306)

“Far from being a specifiable defect of human central nervous system functioning, schizophrenia is the conver­gent motor of cyberpositive escalation: an extraterritorial vastness to be discovered. Although such discovery occurs under conditions that might be to a considerable extent specifiable, whatever the progress in mapping the genetic, biochemical, aetiological, socio-economic, etc. 'bases' of schizophrenia, it remains the case that conditions of reality are not reducible to conditions of encounter.” (p. 308)

“conditions of reality are not reducible to conditions of encounter.” (p. 308)

“It is not merely that schizophrenia is pre-anthropoid. Schizophrenia is premammalian, prezoological, pre-biological ... It is not for those trapped in a constrictive sanity to terminate this regression. Who can be surprised when schizophrenics delegate the question of malfunc:tion? I t is not a matter of what is wrongwith them, but of what is wrongwith life, with nature, with matter, with the preuniversal cosmos. Why are sen.tient life forms crammed into boxes made out of lies? Why does the universe breed en tire populations of prison guards? Why does it feed its broken explorers to packs of dogs? Why is the island of reality lost in an ocean of madness? I t is all very confusing.” (pp. 309-310)

“Capital is not overdeveloped nature, but underdeveloped schizophrenia, which is why nature is contrasted to industrial organization, and not to the escalation of cybertechnics, or anorganic convergence: 'reality ... is not yet constructed' 36 Schizophrenia is nature as cyberpositive mutation, at ·war with the security complex of organic judgment.” (pp. 313-314)

[mathematicianadda]

Where is e hiding in fractals and other iterative systems?

On a strictly conceptual basis, this is what I know:

A) Logorithm = 1/exponential. They are inverse operations. When these operations arise, we enter the realm of "scale." When we measure ∆ in the scale realm, we aren't measuring the change of the list (x1, x2, x3), we're measuring the scalar (read: number) that modifies the list. This is why everything tends towards some infinity or some 0 when we deal with exponential and logorithmic functions. When I hear logorithm or exponential, "e is here" bells start going off.

Ba) Fractals are a new type (or possibly just 'newly decorated type', which is my hypothesis) of way to demonstrate the idea of convergence. We have computers strong enough to show pretty pictures of self-similarity in concrete fashion. In comp sci they call this recursion, iteration, etc. but basically, it's whenever we run f(x0) and then return the output back into the same function as the new x value. This is how cycles and generations work.

Bb) It turns out that fractal patterns dominate any emergent system - especially the the class of emergent systems of which we are most familiar, those found in nature. This is why strange 'islands of stability' pop up when we're dealing with population sizes over time. Pretty much whenever the t variable is present in a system, we allow for emergent properties due to non-linear relationships. This is the land of non-ergodicity and path dependency.

So both fractals and "e" are at the axiomatic core of time series math. And though e is child of 18th century pure mathematics, and fractals are voodoo math invented in the 1960s with the explosion of computational power, they both seem to be mapping the same fundamental principal of 'reality over time.' But, I can't read the map. I'm part-time dyslexic so +∆ of concepts outpaces +∆ of notational skills by a factor of 2<t<3. And I'm impatient bc fractals have changed how I look at the world. Can anyone who speaks the language of this "non-linear" map teach me how to read the legend? Want to learn what's being generalized here...

submitted by /u/Monsieurbreaux [link] [comments] from math https://ift.tt/2vwbapy from Blogger https://ift.tt/31PtBSp

[art-of-mathematics]

Interesting... One of my approaches to correct my cognitive processing via metacognition are very similar... The concept I could finally map fairly detailled some weeks ago, and reading articles on Quantum Bayesian Optimization now. .. well, I see very similar patterns, even with incredible amount of detail considered in both realm...

Emergent properties of error-correction algorithms in non-linear dynamical information systems (as form of self-organization)... could explain the similarity between cognition's underlying non-linear processing patterns - and quantum computing/ quantum information flows / quantum logic in general.

[art-of-mathematics]

Title: "Schrödinger's cat chasing feedback-loops beyond the scope of imagination - transcending contradictions in turbulent logic"

2022/09/26 {∃(¬)s.∀i [Elliot s.AI] | Project: "Detours into philophysics"}

[art-of-mathematics]

chaos theory was my first tattoo.

the first actual theory which changed my life.

my question for you is what is the value of variance and is there a way to predict the variability or the patterns which may form in chaotic systems?

i love your work, it is true art for me

Ohh that is a lovely tattoo!

And I am glad you like my stuff. 👌

I agree, chaos theory has had also a large impact on my -or our, in a way- life.

It is deeply satisfying to see order in chaos, to find elegant simplicity in complexity.

And somehow, for us it has also ensured a feeling of safety and certainty in times of utter lack thereof.

Finding certainty in uncertainty - this brings us closer to your question on variance:

For introduction concepts to answering I can recommend Hermann Haken's stuff on synergetics: self-organization and emergence, which describes that patterns in a system emerge which its elements don't offer themselves. But which patterns, well, my concept about information weaving could explain how information can re-distribute iitself, which might be a part of the answer to your question. Emergence is like a form of "gravity"; quantum gravity, a re-distribution of information density, equivalent in their interpretation to the concept of probabilty intensity distributions in quantum theory. Given that elementary particles are a collection of certain "information geometries" I regard as "complex information weaving sequences", this quantum gravity interpretation is about the distribution of information density in its weaving patterns, and, this is a major leap of thought: The other side of quantum gravity brings us straight to the issue of Navier-Stokes and turbulences, which are, per my interpretation, complex interference patterns, still obeying given 'symmetries' I regard as "butterfly clones" - pairs of possible anthitetic states. (Could also be related to virtual pairs in Feynman diagrams) In a way these turbulences are feedback-loops. The conversation of energy, as in Netwon's second law, "Every action creates a reaction", becomes non-linear, and hence probabilistic and chaotic. And well, this brings us to non-linear causal networks and quantum logic.

Iterative approaches.

And additionally, currently I develop an algorithm that tries to do that - how to 'tackle chaos to unravel itself' - it's a recursive iterative combinatorial approach and highly adaptable to the input you feed it with.

So, to summarize my answer: Predictions might be possible, but I can't say to which degree of exactness and accuracy. Yet, I "sense" a way, and it is primarily "imitating the chaos you want to unravel" - and letting these, the object of study and your imitation of it, interact - somehow you also use self-reference as tool. It's like you throw that chaos in a view between mirrors and it dissects itself.

Lol.

That is literally what happens in LASERs - they are a result of self-organization.

[art-of-mathematics]

https://www.quantamagazine.org/a-math-theory-for-why-people-hallucinate-20180730/

[My thoughts about that exceeding the margin once again.] [Epiphysis dysfunction and elevated bufotenine levels related, as well as a concept of memories being stored as highly compressed mathematical patterns - such turing patterns as raw form of memories - the memory as kind of perfused fractal - associations, analogies and hyperconnectivity - and the brain as literal biological calabi-yau manifold - as highly complex information weaving pattern - related to much of Vijay Balasubramanian's polymathic work ( https://www.quantamagazine.org/pondering-the-bits-that-build-space-time-and-brains-20220420/) and much of my own work regarding non-linear cognition, non-linear axiomatic systems {chaotic processes in axiomatic systems, quantum logic}, information weaving {information (re-)distribution in quantum systems, quantum gravity and how Navier-Stokes relate to that} - all are part of a holistic conception - like each conception/hypothesis is one 2-D shadow of a dynamical 3-D object which is not just moving but also shapeshifting - somehow this netwotk of concepts is like a wavefunction itself, consisting of wavelets and waves... like each puzzle piece is an entire jigsaw puzzle on itself... ]

[art-of-mathematics]

Iteration book

In this art book(let) I want to collect a lot of information about dynamical systems and chaotic processes - and explain iterations by using methods of iteration - with the help of transparent foils. [It explains itself in the way/kind it explains itself, so to speak. [Self-referring recursive loop - I might leap into the topic of Gödel's Incompleteness Theorems and non-linear axiomatic systems occassionally... ] ]

I also want to portray cell division as concrete example - and I also want to include some ideas about Feynman diagrams and explain them as interaction patterns - step by step using transparent foils. --- to render a better understanding of this complex topic about dynamical systems and their axiomatization - and to explain my analogies and neologisms of my concept of "information weaving"

The layers:

[art-of-mathematics]

https://www.quantamagazine.org/the-mystery-at-the-heart-of-physics-that-only-math-can-solve-20210610/

The Mystery at the Heart of Physics That Only Math Can Solve | Quanta Magazine

Interesting article. I would like to add my thoughts about that quote:

"Every other idea that’s been used in physics over the past centuries had its natural place in mathematics. This is clearly not the case with quantum field theory." - Nathan Seiberg, the Institute for Advanced Study

Non-linear axiomatic networks [chaotic processes in non-linear axiomatic systems - say, Quantum Logic] might be the base for the mathematics of QFT - It's time to bring the 21st century in mathematics, I'd say. The mathematics for probabilistic phenomena such as Quantum Mechanics, might not be discovered yet, yet it does not imply it does not exist.

In other words, part of my study deals with Quantum Mechanics being a special threshold or interface between a mathematical reality, entirely information-based, and the physical manifestation thereof. It could explain phenomena such as entanglement and superposition, and furthermore could concretize what a wave function collapse might be - translated into a language human imagination could possibly comprehend.

Somehow the mathematics of quantum mechanics seems intuitive to me - as the life-long analysis of my non-linear cognition is - just that - In plain words, my cognition is the perfect imitation of a quantum computation system. In the recent years, especially months I could continue with my studies on chaotic processes in non-linear axiomatic systems, besides my thesis in the cognitive science sector - about non-linear cognition, a thermodynamic model of the mind, and a "mathematication" of the entire concept of human memories - how they are stored in the brain, and how uncertainty plays an important factor in cognition and memory processing. - This, in return, leads me to many insights regarding quantum logic, turbulences|Navier-Stokes in information distribution, and how it corelates with quantum gravity. [Quantum gravity being an information clustering mechanism]

[art-of-mathematics]

Abstract:

We study the logic of dynamical systems, that is, logics and proof principles for properties of dynamical systems. Dynamical systems are mathematical models describing how the state of a system evolves over time. They are important in modeling and understanding many applications, including embedded systems and cyber-physical systems. In discrete dynamical systems, the state evolves in discrete steps, one step at a time, as described by a difference equation or discrete state transition relation. In continuous dynamical systems, the state evolves continuously along a function, typically described by a differential equation. Hybrid dynamical systems or hybrid systems combine both discrete and continuous dynamics. This is a brief survey of differential dynamic logic for specifying and verifying properties of hybrid systems. We explain hybrid system models, differential dynamic logic, its semantics, and its axiomatization for proving logical formulas about hybrid systems. We study differential invariants, i.e., induction principles for differential equations. We briefly survey theoretical results, including soundness and completeness and deductive power. Differential dynamic logic has been implemented in automatic and interactive theorem provers and has been used successfully to verify safety-critical applications in automotive, aviation, railway, robotics, and analogue electrical circuits.

Published in: 2012 27th Annual IEEE Symposium on Logic in Computer Science

That is really interesting.

Just before I googled it, I tried to summarize my special interests - and it took a few hours, when I gave them the title axiomatization of dynamical systems. (Writing about how I came from my passion for polymath stuff and chaos theory to that would exceed the margin right now.)

Please bare with me, the next stated thoughts might be very ill-formulated gibberish at this stage of thought ...primordial soup or such heeh...

Axiomatization: definition in merriam-webster: the process of reducing down to a system of basic truths or axioms

Let's reduce that idea to basic language using some analogies: (It's very simplified and reduced, many details are omitted.)

Axioms are basic building blocks. Building blocks can be arranged and combined in all sort of ways, like a mosaic. You can chunk them and re-arrange them.

A dynamical system is a chaotic system that changes over time. Its compounds interact. These interactions correlate to the alterations in the dynamical system (compound = subordinate or detail, system = superordinate or whole/big picture)

-> (quantum) contextuality: [Quantum contextuality means the whole alters the details, as well as the details alter the whole. The system alters the compounds, and the compounds alter the system.] [Also: to understand quantum contextuality you can use the example of translating language: One word often has multiple meanings. It is ambigious. Which word is meant in that sentence? The right meaning of the word can be found when the context is analyzed. That is basically the principle behind quantum contextuality: (Also: Good read: https://www.quantamagazine.org/the-spooky-quantum-phenomenon-youve-never-heard-of-20220622/ )] {Further idea in my brain: What is the role of quantum contextuality in quantum error correction algorithms such as Bayesian Optimization?}

Well, back to axiomatization:

A system is a collection of interwoven building blocks. Axiomatization is a process of segmentation, of chunking, and of de-tangling the whole into its basic building blocks.

Dynamical systems are emergent, which means their working mechanisms alter themselves and emerge collectively.

[art-of-mathematics]

Considering starting a 0.75m x1.5m large mindmap again, as my thoughts about non-linear iterative concept development, feedback-loops as recursive error-correction tools, transistion of states regarding binary/certain deterministic and non-binary/uncertain behavior in regards of emergence, and the concept of 'multiple perspectives' and their fusion, literally exceed any margin.

Damn, it all started with logarithmic curves and some concepts about damped vibrations... and where did it end?

Straight into the core of my manifold of incomprehensible entangled theoretical fuckery... Now detangling that semi-literal ball of wool will continue to take forever. Which box of Pandora have I started to open like more than ten years ago?